How many numbers are in the list $$ 1, 4, 7, \ldots, 2005, 2008 ?$$
Adding 2 to each member of the list, we get $$3, 6, 9, \ldots, 2007, 2010,$$ and then dividing each member of the list by 3, we get $$1,2,3,\ldots,669,670,$$ so there are $\boxed{670}$ numbers.